Reverse-Link Capacity of Power-Controlled CDMA Systems With Beamforming

Transcription

1 MITSUBISHI ELECTRIC RESEARCH LABORATORIES Reverse-Link Capacity of Power-Controlled CDMA Systems With Beamforming Jin Yu, Yu-Dong Yao, Jinyun Zhang TR December 2005 Abstract In this paper, reverse-link capacity, in terms of user capacity Erlang capacity, of a directsequence code-division multiple-access (DS-CDMA) system with the use of beamforming is investigated. Signal-to-interference ratio (SIR)-based power control is assumed both transmit receive beamforming are considered. Instead of using tedious iterative methods to evaluate user capacity, a simple closed-form capacity expression with respect to antenna gains, a target SIR, the CDMA processing gain is derived. Numerical results indicate significant capacity improvement with beamforming. The impact of the estimation errors of arrival angles on the capacity is examined. The joint use of a RAKE receiver beamforming is investigated the capacity expression for CDMA systems with multiclass services is also derived. This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors individual contributions to the work; all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c Mitsubishi Electric Research Laboratories, Inc., Broadway, Cambridge, Massachusetts 02139

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3 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 5, SEPTEMBER Reverse-Link Capacity of Power-Controlled CDMA Systems With Beamforming Jin Yu, Student Member, IEEE, Yu-Dong Yao, Senior Member, IEEE, Jinyun Zhang Abstract In this paper, reverse-link capacity, in terms of user capacity Erlang capacity, of a direct-sequence code-division multiple-access (DS-CDMA) system with the use of beamforming is investigated. Signal-to-interference ratio (SIR)-based power control is assumed both transmit receive beamforming are considered. Instead of using tedious iterative methods to evaluate user capacity, a simple closed-form capacity expression with respect to antenna gains, a target SIR, the CDMA processing gain is derived. Numerical results indicate significant capacity improvement with beamforming. The impact of the estimation errors of arrival angles on the capacity is examined. The joint use of a RAKE receiver beamforming is investigated the capacity expression for CDMA systems with multiclass services is also derived. Index Terms Beamforming, code-division multiple access (CDMA), Erlang capacity, power control, RAKE receiver, user capacity. I. INTRODUCTION WITH the advance of wireless communication technology, there is an explosive increase in the number of mobile users. Although second-generation (2G) wireless systems, such as the global system for mobile communications (GSM) IS-95 are successful in many countries [1], they still cannot meet the requirement of high-speed data user capacity in high-user-density areas. Higher system capacity, better quality of service (QoS), flexible accommodations of various wide-b services (such as video multimedia services) with different transmission rates are required in third-generation (3G) wireless communication systems [2]. Code-division multiple access (CDMA) has been chosen as the radio interface technology for 3G systems [3]. Unlike frequency-division multiple access (FDMA) time-division multiple access (TDMA), which are primarily bwidth or dimension limited in capacity, CDMA capacity is interference limited [4]. Thus, any reduction of the interference will directly lead to capacity increases. The emerging technologies, such as beamforming multiuser detections, could lead to a significant reduction in the interference result in many-fold capacity increases Manuscript received December 7, 2002; revised September 10, 2003, January 23, 2004, March 26, 2004, May 7, J. Yu Y.-D. Yao are with the Wireless Information Systems Engineering Laboratory (WISELAB), Department of Electrical Computer Engineering, Stevens Institute of Technology, Hoboken, NJ USA ( jyu@stevens.edu; yyao@stevens.edu). J. Zhang is with the Mitsubishi Electric Research Laboratories (MERL), Cambridge, MA USA ( jzhang@merl.com). Digital Object Identifier /TVT [5] [7]. Capacity estimation is an important element in the design of CDMA systems in the performance evaluation of the new technologies. Gilhousen et al. [4] estimated CDMA reverse-link user capacity, considering voice traffic only, strength-based power control [8], [9] is assumed in the CDMA systems total other-cell interference is modeled as Gaussian noise [4], [10]. increases with the number of active users per cell, which results in a decrease of signal-to-interference ratio (SIR). The maximum can be found considering a target SIR. Using similar methods as [4], Kim Sung estimated the reverse-link user capacity of SIR-based power-controlled CDMA systems in [11] [12]. User capacity of multicode CDMA systems supporting voice data traffic or heterogeneous constant-bit-rate traffic was analyzed in [13]. The effects of a RAKE receiver antenna diversity on reverse-link user capacity are further investigated in [2]. The focus of this paper is to present the user-capacity gain of a SIR-based DS-CDMA system in a multicell multipath fading environment obtained through the use of a RAKE receiver, transmit receive beamforming to derive a simple closed-form expression, which is related to the number of antennas RAKE receiver fingers, a target signal-to-noise-plus-interference ratio (SNIR), the CDMA processing gain, to estimate the reverse-link user capacity. The impact of the estimation errors of the arrival angles (used in beamforming) on the reverse-link user capacity is also examined. In CDMA performance evaluations, the system capacity has also been investigated in terms of Erlang capacity [14], [15], the number of active users is considered to be a Poisson rom variable. Note that the user capacity is used to measure CDMA systems with continuously active users, while Erlang capacity is used to measure CDMA systems with romly active users [16]. Erlang capacity is defined as the average traffic load in terms of average number of users requesting service under a specified blocking probability requirement [14]. In this paper, user capacity is referred to as the number of users that a CDMA system could support at a desired SNIR without power constraints [6]. In this paper, the use of beamforming in CDMA systems is investigated its impact on reverse-link user capacity is first analyzed. Both transmit receive beamforming are considered in the system the joint use of a RAKE receiver beamforming is also examined. The capacity reduction due to the use of beamforming with inaccurate arrival angle estimation is examined. Traffic scenarios such as voice multimedia services are considered in a multiclass CDMA system. A simple closed-form equation, which is related to the antenna array gain patterns, a target SNIR, the CDMA processing /04$ IEEE

4 1424 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 5, SEPTEMBER 2004 gain is given to estimate the reverse-link user capacity. Furthermore, reverse-link Erlang capacity of a CDMA system with beamforming is studied. This paper is organized as follows. System models, including beamforming other-cell interference, are given in Section II. A closed-form expression to evaluate reverse-link user capacity of a CDMA cellular system with beamforming is derived in Section III. Section IV examines the impact of the estimation errors of the arrival angles on the capacity. Section V considers the use of a RAKE receiver Section VI extends the results to multiclass CDMA systems. The Erlang capacity of a CDMA system with beamforming is analyzed in Section VII. Numerical results are given in Section VIII, finally, the conclusion is drawn in Section IX. A. Beamforming II. SYSTEM MODEL Beamforming has been widely used in wireless systems that employ a fixed set of antenna elements in an array. Considering receive beamforming in reverse-link transmissions, the signals from these antenna elements are combined to form a movable beam pattern that can be steered to a desired direction that tracks mobile stations (MSs) as they move. This allows the antenna system to focus radio frequency (RF) resources on a particular mobile station to minimize the impact of interference [17], [18]. This is achieved using a beamformer by placing nulls at the directions of interference, while the antenna array gain in the direction of the desired transmitter is maintained to be constant. While few antenna elements could be installed at an MS, large antenna arrays can be implemented at a base station (BS). When beamforming is used at the MS, the transmit beam pattern can be adjusted to minimize the interference to unintended receivers (such as BSs in other cells). At a BS, receive beamforming for each desired user could be implemented independently without affecting the performance of other links [18]. A linear equally spaced (LES) array is considered here [Fig. 1(a)]. is the azimuthal angle is the elevation angle of a plane wave incident on the array. In this paper, the LES array is used for both transmit receive beamforming. Considering a two-dimensional (2-D) multicell environment (in the horizontal plane) [17], we have. The distance between the elements of the LES array is assumed to be, is the carrier wavelength. In the LES array system, a combining network connects an array of low gain antenna elements could generate an antenna pattern [17], [19] is the number of antenna elements is a variable. The beam could be steered to a desired direction by varying. Considering, an LES array gain pattern is shown in Fig. 1(b). In the remainder of this paper, we will use the antenna pattern specified in (1) to evaluate the impact of beamforming on the CDMA reverse-link capacity. (1) Fig. 1. (a) LES array (b) LES array gain pattern with M =3 =30. B. Other-Cell Interference A cellular structure is shown in Fig. 2 with a reference cell ( ) an interference cell (with BS ). In a CDMA cellular system, an MS is power controlled by a BS in its home cell to ensure that the received SNIR at the BS is no less than a target value, assuming that SIR-based power control is in use. Considering an MS in the interference cell, let the received power at its BS be. Considering the fact that fast fading does not affect the average power level [4], the received interference at the BS of the reference cell can be considered to be [11] are the distances from to, as shown in Fig. 2. is a path-loss exponent. describe the shadowing processes in the cells of the shadowing processes are assumed to be mutually independent follow a lognormal distribution with stard deviation db zero mean. Considering all interfering MSs, the total other-cell interference at is obtained by integrating the whole cellular coverage area except the reference cell [12]

5 YU et al.: REVERSE-LINK CAPACITY OF POWER-CONTROLLED CDMA SYSTEMS WITH BEAMFORMING 1425 Fig. 3. Angle notations in transmit beamforming at MS. in (1), the transmit antenna gain in the direction from is to (3) Fig. 2. Cellular structure reverse-link geometry. Similarly, when receive beamforming is applied with antenna elements at for receiving signals from, the receive antenna gain in the direction from to is if otherwise is the user density per unit area there are MSs in each cell. This assumes that the users are uniformly distributed in a cell that the radius of the hexagonal cell is normalized to unity. is an indicator function to show the cell areas that are excluded in the calculation of, since the MSs in these areas are not power controlled by, but by. In computing the above integral, we simply consider the hexagonal areas of each cell rather than the actual coverage area of the BSs [4], [11], [12]. III. DERIVATION OF REVERSE-LINK USER CAPACITY When beamforming is applied at both transmit receive sides, the total other-cell interference at can be expressed as The expected value of the total other-cell interference is which can be rewritten as with (4) (5) (2) are transmit receive beamforming gain patterns. are the azimuth angle of to its home BS that to, respectively. is the distance between. is the azimuth angle of to. is the azimuth angle of MS to, as shown in Fig. 2, is uniformly distributed from 0 to. Fig. 3 indicates angle notations in transmit beamforming at. When antenna elements are used with the beamforming pattern shown

6 1426 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 5, SEPTEMBER 2004 Similarly, the variance of is expressed as which, following [4], is rewritten as (6) Fig. 4. Angle notations of receive beamforming at BS. unity since their transmit beams are steered toward BS. is the azimuth angle of an interfering MS to. Fig. 4 illustrates angle notations of receive beamforming at. is the receive beamforming gain of to the direction of. are uniformly distributed in. Let ; the probability density function (pdf) of is found to be We further have otherwise. The value,, can be obtained numerically. For example, when only the first- second-tier cells are considered, we find, for, db,,,,,. In CDMA systems, the received SNIR should be no less than a target value in order to maintain a required transmission quality. Following [2] [11] considering transmit receive beamforming, we have is the CDMA processing gain, is the single-sided white noise power spectrum density, is the spreading bwidth. The factor 2/3 in the denominator is due to the assumption of a square chip pulse. The denominator in (7) includes other-cell interference as well as own-cell interference due to other MSs in the reference cell. Note that the transmit antenna gains of MSs at the reference cell in (7) are all set to (7) Let be the minimum power level satisfying (7). The received power could be expressed in terms of as Now, the user capacity can be found via an iterative method [2], [11], in which there are two concatenated iteration loops. In the inner loop, for a given value, determine using the following steps. Step 1) Set as zeros. Step 2) Calculate from (8). Step 3) Calculate from (5) (6). Step 4) Repeat Steps 2) 3) until the differences between old new values of are less than 1% [2]. Using the obtained above a specified maximum transmission power limit, calculate an outage probability (the transmission power exceeds the power constraint) [2]. If the outage probability does not exceeds a required level, the outer loop increases by 1 enters the interloop. The iteration loops stop when the calculated outage probability exceeds the required level. We then obtain the user capacity as. (8)

7 YU et al.: REVERSE-LINK CAPACITY OF POWER-CONTROLLED CDMA SYSTEMS WITH BEAMFORMING 1427 The iterative method to determine user capacity as described above is computationally complicated due to multiple loops of numerical integrations. In this paper, we derive a formula to directly estimate user capacity, which is related to all the relevant factors, such as, beamforming gains, CDMA processing gains. Solving (5), (6), (8), we get Thus, we have with (9) (10) It is obvious that are greater than 0 because the noise or interference power is always positive. Thus, a valid has to ensure that (9) (10) are greater than 0. As shown in Appendix A, we are able to determine user capacity as (11) indicates maximum integer no greater than.in using the iterative method to determine the user capacity, we found that when the number of users is above the user capacity, power control will not work, since every MS tries to satisfy the target SNIR by increasing its transmit power until reaching its maximum transmit power allowed. This leads to an increase of interference to other users. The results from the closed-form expression (11) will be compared in Section VIII with those results obtained from the iterative method. IV. IMPACT OF DoA MISMATCH In this section, the impact of direction of arrival (DoA) mismatch on the capacity is analyzed. The arrival angle,, can be characterized as a rom variable with a uniform distribution or a normal distribution [20], is the exact arrival angle of the desired user, which is also the mean value of, due to the uniform or normal distribution of the DoA estimation errors. The SNIR with DoA mismatch assuming that perfect power control can be derived as (12) unif. norm. is the exact arrival angle represents the variance of the angle estimation errors. Assuming perfect transmit power control, the transmit power of the th user in other cell is represents the exact arrival angles of the th user of the reference cell. Similarly, since all the users are uniformly distributed in the cell, the expected gain have to be averaged throughout the whole cell area. Considering the conditions, the reverse-link capacity with DoA estimation errors can be found to be is the estimated departure angle of the th user in other cell represents the estimated arrival angle of the desired user. Therefore, the total interference is (13) Note that the issue of angular spreads is not addressed here. For rural environments, angular spreads between 1 5 have been observed [21]. For urban hilly terrain environments, considerably larger angular spreads, as long as 20, have been found [22]. The impact of the angular spread on CDMA capacity will be investigated in future studies.

8 1428 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 5, SEPTEMBER 2004 V. CONSIDERATION OF THE RAKE RECEIVER Multipath propagation in the radio channel leads to deep fading of the received signal. If the paths are independent resolvable in time domain, i.e., the delay between different paths is greater than the chip duration, a RAKE receiver can be used to combine the paths to achieve diversity gains [15]. The multipath fading can be characterized by a power delay profile (PDP), which is uniformly or exponentially distributed [2]. For a uniform PDP, we have for an exponential PDP we have is the square path gain of the th path follows an exponential distribution (its envelop is Rayleigh distributed), is the total number of paths in a uniform profile, is a decay factor for an exponential profile. Assuming that the RAKE receiver at the BS has fingers, the received power at the output is the combination of the paths. Following [2], (5), (6), (7) are modified as (14) (15) users requiring varying date rates for different applications. In the multiclass CDMA system, a single code can be assigned to each service (such as audio, data, video services) with different processing gains. This differs from multicode CDMA [23], which can also be used to realize the multiclass CDMA. Heterogeneous constant-bit-rate (CBR) traffic, such as audio, data, video services, are considered in this paper, which are assigned different spreading codes with processing gains,,, respectively. For example, we could assume that spreading gains for audio, data, video traffic are 128, 64, 32, respectively. In this way, the services with different rates are accommodated with spreading sequences with various lengths or processing gains. If the processing gains are normalized by, we obtain the normalized processing gains for audio, data, video services,,. The total other-cell interference comes from all the traffic types is [11]. If the traffics are assumed to be independent of each other, we could get (18) (19) Note that three types of spreading sequences with different processing gains,,,, are used to meet the requirement for different rates. Furthermore, in order to meet SNIR requirements (,, ) for different services, the corresponding transmission power is controlled to obtain the required received power for each service (,, ). And different traffic types have to satisfy the different SNIR requirements for uniform PDP for exponential PDP. We can get the expression of in terms of when SNIR satisfies the minimum requirement (16) Considering using (14) (16), the user capacity with a joint use of a RAKE receiver beamforming can be derived as subscripts,, represent audio, data, video traffic types, respectively. (,, or ) represent the corresponding user capacity target SNIR, respectively. Let,, be normalized received power,,. We rewrite the above equation as (17) VI. ANALYSIS OF MULTICLASS CDMA In Section III, we derived the user capacity in a flat-fading environment. Multipath propagation (resolvable multipaths) the use of a RAKE receiver are considered in Section IV. In this section, we extend the results to a CDMA system with multiclass operation. Multiclass CDMA is a method to support (20) We could get the minimum required received power (normalized),, when we set the received of different traffic equal to their target values. Following [11] [24]

9 YU et al.: REVERSE-LINK CAPACITY OF POWER-CONTROLLED CDMA SYSTEMS WITH BEAMFORMING 1429 solving (20),,, could be expressed in terms of the total other-cell interference as which is equal to the ratio of noise power to total noise-plus-interference power, when. The ratio of other-cell interference to own-cell interference plus signal power is Let. Following (21), we have. Now, we consider that a CDMA system has romly active users with Poisson arrivals (mean call arrival rate ) exponential service time (mean call duration time ). A newly arrived user is blocked when, therefore, we have the blocking probability for a CDMA system Based on the derivations in Section III, the user capacity for a multiclass CDMA system in a flat fading channel is found as (21) When a multipath fading environment with resolvable paths is considered a RAKE receiver is used in the multiclass CDMA system, the user capacity can be derived as (22),, are the same as given in Section V. VII. ERLANG CAPACITY As discussed in Section I, the user capacity is used to measure CDMA systems with continuously active users Erlang capacity is used to measure CDMA systems with romly active users. We consider a system with a Poisson arrival exponential service time in the Erlang capacity evaluation [24]. In Sections III V, we investigated the user capacity over CDMA reverse links. In this section, we focus on the Erlang capacity consider the use of beamforming. Based on (7), total interference including own- other-cell interference is we have According to [14], the rom variable can be approximated using the central limit theorem. The blocking probability is then (24) The mean variance of can be obtained considering that, although the total number of other-cell users is generally much larger than that from a single cell, their average power is equivalent to that of users [14]. The mean variance of are increased by a factor, compared with own-cell interference Substituting (25) (26) into (24), we get (25) (26) (27) Equation (27) gives the expression for reverse-link Erlang capacity of a CDMA system with beamforming, which relates to the call-blocking probability, target SNIR, CDMA processing gain, expected antenna gain. which can be rewritten as (23) VIII. NUMERIC RESULTS Throughout this section, we assume propagation parameters db. Table I lists multiclass CDMA system parameters. The basic data rate is assumed to be 32 Kb/s the spreading chip rate is Mb/s. The first traffic type is of the basic rate its required SNIR target is 5 db. The

10 1430 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 5, SEPTEMBER 2004 TABLE I SYSTEM PARAMETERS TABLE II COMPUTATIONAL PARAMETERS WITH M =1 TABLE III COMPUTATIONAL PARAMETERS WITH M =2 Fig. 5. User capacity. (a) Effect of beamforming (b) per receive antenna element. second third traffic types require higher data rates ( Kb/s) their SNIR targets are 10 7 db, respectively. Table II considers a single transmit antenna element, at the receive side, the number of antenna elements varies from 1, 3, 5, 7, to 9. As is proportional to other-cell interference, we see that the value of decreases with an increase of the number of receive antenna elements,. The received own-cell interference is proportional to the expected received antenna gain, which decreases with increasing,as shown in Table II. The values of are also presented in this table, which will be used in evaluating user capacity via the iterative method, as described in Section III. The values of are to be used in evaluating the multiclass CDMA system. Table III is similar to Table II, except that various numbers of transmit antenna elements are considered. A. User Capacity of CDMA Fig. 5 presents the reverse-link user capacity with beamforming illustrates the effect of the number of receive antenna elements. Fig. 5(a) clearly shows that the user capacity increases significantly when the number of antenna elements increases. However, as shown in Fig. 5(b), the user capacity per antenna drops with the increase of antenna elements. In Fig. 5(a), we also compare the capacity evaluations using a simple closed-form expression (11) those based on the complex iterative method, the outage probability, as discussed in Section III, is assumed to be 0.05 [2]. Almost identical capacity results are obtained using the two evaluation methods. Based on numerical calculations, for some cases, they give identical results. In some other scenarios, they only differ by one user in capacity evaluations. For example, when, from (11) we obtain. When the iterative method is used, we get, which corresponds to an outage probability of However, a close examination reveals that the system with 145 users is not sustainable (not practical), since the mean other-cell interference Fig. 6. User capacity, impact of antenna element distribution between the transmitter receiver. reaches. Note that, when,wehave. Recall that the simple closed-form expression is derived in Section III to evaluate user capacity. Fig. 5(a) illustrates the effectiveness accuracy of this approach. Fig. 5 presents the capacity results of single-code CDMA systems, which are also applicable to multiclass CDMA systems when let, (11) (21) are identical. This suggests that once is calculated, the values of can be determined by a BS according to. For a fixed number of total antenna elements,itis interesting to determine the distribution of antenna elements between the transmit receive sides to maximize user capacity. Fig. 6 presents the capacity results when 4, 6, 8, 10. When, it is seen that maximum capacity is achieved when,. For cases with 6, 8, 10, maximum capacity is achieved when 2. The numerical results indicate that, to obtain higher reverse-link user capacity, it is desirable to put more antenna elements at the receive sides (BS) compared to the transmit side

11 YU et al.: REVERSE-LINK CAPACITY OF POWER-CONTROLLED CDMA SYSTEMS WITH BEAMFORMING 1431 Fig. 7. User capacity, impact of DoA estimation errors. (a) Uniform distribution (b) normal distribution. (MS). The numerical results also suggest that when is small, say 4, only one antenna element should be placed at the transmit side. When increases to 6, 8, or 10, two antenna elements should be used at the transmit side. With further increasing, it is expected that the number of antenna elements at the transmit side should be increased. B. User Capacity Considering DoA Estimation Errors The capacity with beamforming considering DoA estimation errors can be evaluated using (13) the corresponding numerical results of user capacity are shown in Fig. 7(a) (b), the number of transmit antenna elements is set to be two that of receive antenna elements varies from 1 to 9. Both normal [Fig. 7(a)] uniform [Fig. 7(b)] distribution of the estimated DoA errors are considered, in which varies from 2 to 4. It is observed that the capacity reduction increases with increased estimation errors. Since the beamwidth becomes narrower with increased number of receive antenna elements, the same errors can lead to a significant reduction of the capacity when is larger. Fig. 8. User capacity, effect of beamforming RAKE receiver. (a) Uniform PDP. (b) Exponential PDP. C. User Capacity of CDMA With Beamforming RAKE Receiver When both beamforming a RAKE receiver are used, the reverse-link user capacity can be evaluated using (17). Assuming a multipart environment with, the numerical results of user capacity are presented in Fig. 8(a) (b). Both uniform [Fig. 8(a)] exponential [Fig. 8(b)] PDPs are considered. For comparison, the number of transmit antenna elements is set to be 1 2 the number of RAKE receiver fingers varies from 2, 3 to 4. Noticeable capacity improvements are seen when the number of RAKE receiver fingers increases, which indicates the effectiveness of the RAKE receiver in combination with the use of beamforming. Fig. 9. Erlang capacity of a CDMA system with beamforming. D. Erlang Capacity of CDMA With Beamforming Erlang capacity due to different number of antenna elements at both transmit receive sides are shown in Fig. 9. We consider db. Following [14], the ratio of noise power to total noise-plus-interference power is assumed to be 0.1. It is seen that Erlang capacity increases with

12 1432 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 5, SEPTEMBER 2004 an increase of the number of antenna elements at either side of the system. Given the Erlang capacity, we are able to calculate the number of users that a system can support under a specified call-blocking rate traffic load. If the traffic load of each user is 0.1, the system could support users dynamically with. IX. CONCLUSION A simple closed-form expression is derived to evaluate reverse-link user capacity for CDMA multiclass CDMA systems with beamforming a RAKE receiver in multipath fading multicell environments. The impact of the DoA estimation errors is also considered. The reverse-link Erlang capacity, which quantifies the dynamic traffic characterization, is analyzed. Both transmit receive beamforming are assumed in the system significant capacity improvements are observed with an increase in the number of antenna elements. The capacity improvement due to the RAKE receiver is also illustrated. The relationships between the capacity various system parameters, including the target SNIR, CDMA processing gain, antenna array gain patterns, the number of RAKE receiver fingers, are reflected in the simple closed-form capacity equations. In this paper, we consider an LES array for beamforming. The developed capacity evaluation method can be applied to CDMA systems with other types of arrays by considering different transmit receive array gain patterns. Perfect fast transmit power control is assumed in this paper. In a practical system, the loop delay of power control the accuracy of SNIR estimation will have an impact on the performance of power control, which reduces the CDMA capacity. Furthermore, in a multipath environment, signals arrive at the receiver through multiple paths from different directions (angular spreads), which will increase the complexity to steer the beam toward each direction. All these practical issues affecting the system capacity will be studied in the future. which gives And if, from (29) Let substitute it into (31) Solving (32), we get It is easily shown that Due to,,,, we get Thus (30) (31) (32) (33) (34) (35) (36) Combining (30) (36), has to satisfy APPENDIX A DERIVATION OF (11) Equations (9) (10) have to satisfy the following two conditions: (28) (29) (37) If, from (30), (32), (33), (34) we could conclude that there is no that satisfies (28) (29) simultaneously. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their valuable comments. Using (28) considering the fact that, we get REFERENCES [1] J. E. Padgett, C. G. Gunther, T. Hattori, Overview of wireless personal communications, IEEE Commun. Mag., vol. 33, pp , Jan

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Toeltsch et al., Statistical characterization of urban spatial radio channels, IEEE J. Select. Areas. Commun., vol. 20, pp , Apr [23] J. Chen, J. Wang, M. Sawahashi, MCI cancellation for multicode wideb CDMA systems, IEEE J. Select. Areas. Commun., vol. 20, pp , Feb [24] Z. Liu, M. J. Karol, M. E. Zarki, K. Y. Eng, A dem-assignment access control for multicode DS-CDMA wireless packet (ATM) networks, in Proc. IEEE INFOCOM 96, San Francisco, CA, May 1996, pp Jin Yu (S 01) received the B.S.E.E. degree from Wuhan University, China, in 1998, the M.S.E.E. degree from the University of Mississippi, Oxford, in 2001, is currently working toward the Ph.D. degree in electrical engineering at Stevens Institute of Technology, Hoboken, NJ. During his study at the University of Mississippi, his research work focused on the computational electromagnetics microwave circuits. At present, he is doing research in the applications of phased arrays in wireless communications at the Wireless Information Systems Engineering Laboratory (WISELAB), Stevens Institute of Technology. His research interest areas include code-division multiple access (CDMA), signal processing for wireless communications, adaptive antennas. Yu-Dong Yao (S 88 M 88 SM 94) received the B.Eng. M.Eng. degrees from Nanjing University of Posts Telecommunications, Nanjing, China, in , respectively, the Ph.D. degree from Southeast University, Nanjing, China, in 1988, all in electrical engineering. From 1989 to 1990, he was with Carleton University, Ottawa, ON, Canada, as a Research Associate working on mobile radio communications. From 1990 to 1994, he was with Spar Aerospace Ltd., Montreal, PQ, Canada, he was involved in research on satellite communications. From 1994 to 2000, he was with Qualcomm Inc., San Diego, CA, he participated in research development in wireless code-division multiple-access (CDMA) systems. He joined the Stevens Institute of Technology, Hoboken, NJ, in 2000, he is an Associate Professor in the Department of Electrical Computer Engineering a Director of the Wireless Information Systems Engineering Laboratory (WISELAB). He holds one Chinese patent eight U.S. patents. He was a Guest Editor for a Special Issue on wireless networks for the International Journal of Communication Systems. His research interests include wireless communications networks, spread spectrum CDMA, DSP for wireless systems. Dr. Yao is an Associate Editor of IEEE COMMUNICATIONS LETTERS IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY an Editor for IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS. Jinyun Zhang received the Ph.D. degree in electrical engineering from the University of Ottawa, Ottawa, ON, Canada, in She was with Nortel Networks for more than 10 years, she held engineering management positions in the areas of very-large-scale integration (VLSI) design, advanced wireless technology development, wireless optical networks. She currently is a Senior Principal Technical Staff Member Group Manager of the digital communication networking group with Mitsubishi Electric Research Laboratories (MERL), Cambridge, MA, she manages many wireless communications networking projects, including UWB, IEEE802.11WLAN, ZigBee, sensor network, 3G/4G wireless communications.